Weather forecast uncertainty arises from imperfect analyses and forecast models, but ensemble spread alone does not reveal how distinct sources relate to downstream targets. We introduce Pangu-Bayes, a probabilistic forecasting hierarchy that treats atmospheric-state and learned-model uncertainty as distinct stochastic variables, crossing flow-dependent perturbations of the evolving state with Bayesian parameter samples. This construction yields model-defined source-resolved variance components and matched pathway evaluation. Across 90 held-out 2023 tropical cyclones, Pangu-Bayes reduces track, pressure and wind errors by 54.2%, 17.2% and 24.9%, respectively, while improving rapid-intensification detection. Among 88 cyclones supporting pathway comparison, atmospheric-state variability is more consistently associated with improved track prediction, whereas learned-model variability is more often associated with improved intensity prediction. During Mawar and Khanun, state perturbations sample alternative steering-flow evolutions associated with recurvature, whereas parameter sampling broadens intensity evolution. Pangu-Bayes thus connects model-defined uncertainty resolution to target-dependent value and dynamical interpretation while retaining competitive global probabilistic skill.

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